Download Adv. Inorganic Chemistry

Crystal-field theory
This is an early theory of electronic structure of complexes especially for the properties of
transition metal ions in ionic crystals. The model of an octahedral complex is used, with six
ligands placed on the Cartesian axes centered on the metal ion. The ligands interact strongly
with the central metal ion.
1. Ligand field splitting parameters
symmetry type: eg (3/5Δo above the average energy)
- d-orbitals pointing directly along the Cartesian axes and
directly at the ligands
=> the electrons are repelled more strongly by the ligands
=> orbitals are doubly degenerate
symmetry type: t2g (2/5Δo below the average energy)
- d-orbitals that point between the ligands
=> electrons are less repelled by the ligands
=> orbitals are triply degenerate
This leads to an energy diagram in which the t2g orbitals lie below the eg orbitals. The
separation (energy difference) is called “ligand field splitting parameter” Δo (O: stands for
octahedral)
2. Spectrochemical series
The ligand field splitting parameter (Δo) varies systematically with the kind of ligands. In the
spectrochemical series the ligands are arranged in order of increasing energy for the splitting
of the d orbitals (higher optical absorption). The values of Δo also depend on the metal ion
with two important trends: Δo increases with increasing oxidation number and increases down
a group. Δ o depends also on the row of the metal ion in the periodic table and normally
Δo(5d) >Δo(4d) > Δo(3d).
=> spectrochemical series of ligands:
I-< Br-< S2-< SCN-< Cl-< NO3-< N3-< F-< OH-< C2O42-< H2O < NCS-< CH3CN< py <NH3<
en< bipy< phen< NO2-< PPh3< CN-< CO
=> spectrochemical series of metal ions:
Mn2+< Ni 2+< Fe2+< V2+< Fe3+< Co3+< Mn4+< Mo3+< Rh3+< Ru3+< Pd4+< Ir3+< Pt4+
3. High spin and low spin complexes
low spin complex: species with smaller number of parallel electron spins
high spin complex: species with the greater number of parallel electron spins
Ligand field stabilization energy (LFSE) is the net energy of a t2gxegy configuration. It is
relative to the average energy of the orbitals with: LFSE= (-0.4x+0.6y) Δo
For the lowest energy configuration the Pauli Exclusion Principle and if possible the Hund’s
rule have to be respected. The ground state configuration for dn configurations with n= 1, 2, 3
and also for n= 8, 9, 10 complexes is unambiguous because there is no competition between
LFSE and pairing energy. There are two possibilities for dn configurations with n=4, 5, 6, 7:
the high spin and the low spin configuration. The strength of the crystal field (Δo) and the spin
pairing energy (P) depend on the identity of both metal and ligands and it is not possible to
specify a point in the spectrochemical series at which a complex changes from high spin to
low spin.
e.g. d4 elements :
1.) High spin : three 3d electrons occupy separate t2g and one electron occupies one of the eg
orbitals -> pairing penalty avoided
LFSE= 3x (-0,4Δo)+ 0,6 Δo= -0,6 Δo
2.) Low spin : all electrons occupy the t2g orbitals so that one of them is occupied from two
electrons -> strong coulomb repulsion: “pairing energy” (P)
LFSE= 4x (-0,4Δo)= -1,6Δo
- net stabilization= -1,6Δo-P
Δo<P= “weak-field case”: - lower energy is achieved if the upper orbital is occupied: t2g3 eg1
configuration e. g. [Cr(OH2)6]2+ (high spin complex)
Δo>P= “strong field case”: - lower energy is achieved by occupying only the lower orbitals
despite the cost of the pairing energy: t2g4 configuration e.g. [Cr(CN)6]4- ( low spin complex)
4. Color of transition metal complexes
The color of transition metal complexes is related to the excitation of the d-electrons from the
t2g state to the eg state. The splitting of the d orbitals is directly related to the energy of the
absorbed light. The color of the complex is the complementary color of the absorbed light.
[Ni(NH3)6]2
[Ni(H2O)6]2+
Green
Blue
Color of the complex
Red
Yellow
Absorbed light
small
Larger as for [Ni(H2O)6]2+
Splitting
References:
P. Atkins, T. Overton, J.Rourke, M. Weller, F. Armstrong, Shriver & Atkins ‘Inorganic
Chemistry, 5th edition, 2010, Oxford University Press, Oxford.
E. Riedel, Anorganische Chemie, 6. Auflage, 2004, Walter de Gruyter, Berlin
Further tasks:
I. Apply the crystal-field theory for octahedral complexes on a d6 configuration. Give a
possible example and calculate the LFSE.
II. Explain the difference of high and low spin complexes.